Question

The coefficient of friction between two blocks of masses 1 kg and 4 kg as shown in figure is $\mu$ and the horizontal plane is smooth. If the system is slightly displaced and released it will execute S.H.M. The maximum amplitude if the upper block does not slip relative to lower block will be (k is spring constant)

• A. $\frac{5\mu g}{k}$
• B. $\frac{\mu g}{k}$
• C. $\frac{3\mu g}{k}$
• D. $\frac{2\mu g}{k}$

Answer 1

The correct option is A $\frac{5\mu g}{k}$

For no sliping over block M,

$f_r\ge ma$

$f_r=$Frictional force between the blocks

$f_r=\mu mg$

$a\le \mu g$ or $a=\mu g$

$kx-f_r=Ma$

$kx-\mu mg=M\mu g$

$kx=5\mu g$

$x=(\frac{5\mu g}{k}$)=Amplitude.